Question

in quadrilateral abcd, ad || bc. what must the length of segment ad be for the quadrilateral to be a parallelogram? 3x + 7, 5x - 9. 8 units, 16 units, 31 units, 62 units

Explanation:

Step1: Recall parallelogram property

In a parallelogram, opposite - sides are equal. Here, $AD$ and $BC$ are opposite sides. So, $3x + 7=5x−9$.

Step2: Solve for $x$

Subtract $3x$ from both sides:
$3x + 7-3x=5x−9 - 3x$
$7 = 2x-9$.
Add 9 to both sides:
$7 + 9=2x-9 + 9$
$16 = 2x$.
Divide both sides by 2:
$x=\frac{16}{2}=8$.

Step3: Find the length of $AD$

Substitute $x = 8$ into the expression for $AD$ which is $3x + 7$.
$AD=3\times8 + 7=24 + 7=31$.

Answer:

31 units